Considerations of Efficiency and Distributive Justice in Multidimensional Poverty Measurement

Distributive Justice in Multidimensional Poverty Measurement

Dissertation

zur Erlangung des Doktorgrades der Wirtschaftswissenschaftlichen Fakultät

der Georg-August-Universität Göttingen

vorgelegt von Nicole Isabell Rippin

geboren in Bonn, Bad-Godesberg Göttingen 2013

Gutachter:

Prof. Stephan Klasen, Ph.D.

Universität Göttingen

J-Prof. Dr. Sebastian Vollmer

Universität Göttingen

1. Die Gelegenheit zum vorliegenden Promotionsvorhaben ist mir nicht kommerziell vermittelt worden. Insbesondere habe ich keine Organisation eingeschaltet, die gegen Entgelt Betreuerinnen und Betreuer für die Anfertigung von Dissertationen sucht oder die mir obliegenden Pflichten hinsichtlich der Prüfungsleistungen für mich ganz oder teilweise erledigt.

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Nicole Isabell Rippin

The twentieth century brought a lot of change for welfare economics that resulted in a profound transformation of poverty measurement. It began in the nineteen-thirties and –fifties when two waves of severe criticism concerning the comparability of individual utilities posed a serious threat to the long history of utility-based welfarism. For a transitional period the income approach moved into the centre of traditional theory. Though mostly considered as a mere placeholder until a new theory of welfare economics would take over, it should become the main approach to poverty measurement.

The situation changed with the development of the capability approach from the nineteen-eighties onwards; the first approach that actually had the potential to establish a new theory of welfare economics. The new approach made capabilities and functionings, i.e. what persons are actually able to do and be, the subject of analyses rather than economic resources or utility. Poverty under this approach is the failure to achieve a minimum set of central capabilities needed in order to be able to pursue whatever one has reason to value in life. This definition already indicates the approach’s inherent respect of individual freedom and responsibility that makes it especially intriguing. The latter, however, becomes most obvious in the case of inequality.

The objective of distributive justice within the framework of the capability approach is to remove inequality of opportunity in order to create a level playing field that enables every individual to pursue whatever he or she has reason to value. Inequality of choice or effort is explicitly excluded. The clear distinction between the two types of inequality acknowledges the tension between distributive justice and efficiency, the objective of the latter being the expansion of the overall capability set available in a society. This distinction, though crucial, is seldom made in welfare economic theory.

Despite all its strengths, the capability approach faced a lot of resistance, mainly due to the fact that it replaces the subject of analysis, utility or income, with a set of subjects that are all measured in different units. Thus, a lot of scepticism was raised with regard to its operationalisability which obviously required a multidimensional approach. However, the initial resistance weakened over time. By now, new multidimensional indices are proposed on

an almost daily basis. Interestingly, the new multidimensional approach is not only utilised to operationalise the capability approach, but also traditional welfarism. It seems that due to the sudden availability of the new multidimensional measures the latter experiences a rather unexpected resurrection.

The main objective of this volume is to analyse in how far the decision to define and measure poverty in terms of one of the three main theories of welfare economics that define well-being either as i) happiness (traditional welfarism), ii) opulence (income or expenditure approach), or iii) capabilities and functionings (capability approach) affects the empirical evaluation of poverty and poverty trends.

However, in order to be able to do so, a methodological weakness inherent in the current multidimensional approach to poverty measurement has to be addressed first. As mentioned before, one of the main strengths of the capability approach is that it explicitly accounts for the tension between the two concepts of distributive justice and efficiency (Sen, 1992, pp. 7- 8):

‘But equality is not the only social charge with which we have to be concerned, and there are demands of efficiency as well. An attempt to achieve equality of capabilities – without taking note of aggregative considerations – can lead to severe curtailment of the capabilities that people can altogether have. […] Indeed, it will be argued that the import [sic!] of the concept of equality cannot even be adequately understood without paying simultaneous attention also to aggregative consideration – to the ‘efficiency aspect’ […].’

One could easily consider distributive changes that are just but not efficient and vice versa.¹ Nevertheless, in the current approach to multidimensional poverty measurement, this crucial difference is not made: inequality between poverty dimensions is generally treated as association sensitivity, thus reducing the concept of distributive justice to a mere analysis of how efficient poverty deprivations are distributed among the poor.

The first two essays of this volume are dedicated to overcome this methodological weakness. Starting point is the suggestion to define inequality between dimensions more

1 As a simple example consider the distribution of six pairs of shoes between two persons. Initially, person 1 has five right shoes and one left shoe, whereas person 2 has one right shoe and five left shoes. Since left and right shoes are perfect complements, both persons are able to wear exactly one pair of shoes. This situation satisfies the concept of distributive justice. However, it is obvious that it is far from being efficient: through a simple switch of shoes both person could have three pairs each – a situation that still satisfies the concept of distributive justice. On the other hand, a switch of shoes that leaves person 1 with one right and one left shoe and person 2 with five right and five left shoes would satisfy the concept of efficiency but would violate the concept of distributive justice.

holistically as the association-sensitive spread of simultaneous deprivations across the population.

The first essay deals with the operationalisation of the extended definition of inequality between dimensions in the case of ordinal poverty indices. It introduces a new property called

“Sensitivity to Inequality Increasing Switch (SIIS)” that conditions the extent to which an inequality increasing switch increases poverty on the relationship between poverty dimensions. The new property is utilised to derive a new class of multidimensional poverty indices that is unique in the sense that it is the first class of additive poverty indices that is able to account for inequality as well as association-sensitivity.

The second essay does essentially the same with regard to cardinal poverty indices. It introduces a new property called “Inequality Sensitivity (IS)” that basically requires poverty to increase (in the case of substitutes) or to decrease (in the case of complements) if an association increasing switch between two poor individuals comes at the expense of the poorer of the two. Again, the new property is utilised to derive a new and unique class of multidimensional indices that, though additive, is able to account for both inequality within and between poverty dimensions on one hand and the relationship between poverty dimensions on the other.

Once the methodological weakness has been corrected, the third essay uses the rich data source of the German Socio-Economic Panel in order to propose a new (ordinal) multidimensional poverty index for Germany that is based on the capability approach, the so called German Correlation Sensitive Poverty Index. It also introduces a multidimensional happiness index, the Subjective Correlation Sensitive Poverty Index, that is based on traditional welfarism and is derived from a satisfaction-based self-evaluation of different poverty dimensions. Finally, the official poverty measure of Germany, i.e. the at-risk-of- poverty rate, defined as 60 per cent of the median net equivalence income, is calculated as a representative of the income approach. All three indices are compared across dimensions, regions and over time, and the results seem to indicate one thing above all: the significant differences in the evaluation of poverty and poverty trends induced by the different indices and the high added value that is created through the operationalisation of the capability approach.

This thesis would not have been possible without the support of many persons who contributed in one way or another to its completion.

First and foremost, I want to thank my supervisor Professor Stephan Klasen for giving me the opportunity to write this thesis as an external PhD student. I am well aware that this is something not many professors would be willing to do as it means a lot of work while getting little in return. I decided to approach Stephan Klasen because of what I knew about his excellent scientific reputation but I got much more than I expected. It never ceases to amaze me how he skilfully managed to give me all freedom to do my own research and follow my ideas while at the same time providing the best possible support whenever needed. I am more than grateful.

As well, I would like to express my deepest thanks to my second supervisor Junior Professor Sebastian Vollmer for carefully reading and commenting on several revisions of my writings. This thesis benefited greatly from his insightful comments and constructive criticism, and his practical advice and kind encouragement were a great support especially at the final stage of the work.

My heartfelt thanks also go to my colleagues at the German Development Institute, especially Tilman Altenburg and Markus Loewe, for understandingly releasing me from tedious tasks and for patiently enduring me in stressed mood. I could not imagine a better working atmosphere.

I am also very thankful to Sabina Alkire, Eva Jespersen, Stephan Klasen, and Peter Krause for facilitating my research stays at the Oxford Poverty and Human Development Initiative, the Human Development Report Office, the University of Göttingen, and the German Institute for Economic Research, respectively, as well as, of course, their whole staff.

My research benefited greatly from the deep knowledge that they readily shared and their openness and friendliness made the resarch stays an experience that I will always treasure.

I also wish to thank the many scientists who helped me with their valuable comments and suggestions all along the way, in particular Valérie Bérenger, Florent Bresson, Satya Chakravarty, Conchita D’Ambrosio, Markus Grabka, Ortrud Leßmann, Milorad Kovacevic,

Jacques Silber, Subbu Subramanian, Suman Seth, Maria Emma Santos, Casilda Lasso de la Vega, Gaston Yalonetzky and several anonymous referees.

In addition, I would like to thank the participants of the following conferences for their helpful comments and suggestions: the Human Development and Capability Association’s annual conference (Amman, 2010; The Hague, 2011; Jakarta, 2012), the Fourth Meeting of the Society for the Study of Economic Inequality (Catania, 2011), the OECD Universities’

Joint Economics Congress: New Directions in Welfare II (Paris, 2011), the Research Committee of the German Economic Association on Development Economics’ annual conference (Bonn, 2012), and the 32^nd International Association for Research in Income and Wealth conference (Boston, 2012).

The financial assistance of the German Federal Ministry for Economic Cooperation and Development is gratefully acknowledged.

Last but in no way least, I am most grateful to all my friends, in particular Mario, Andreas, Julia, Jimmy and Josefa, whose readiness to listen was a great support especially during the hard times. I also want to thank my wonderful family, in particular my grandparents and parents, who always believed in me and continuously encouraged me to reach higher. Finally, my deepest thanks go to my husband whose love gave me stability and carried me through times of crisis. Without his continuous support I could not have done any of this.

List of Abbreviations ... xi

List of Figures ... xiii

List of Tables ... xiv

Introduction ... 1

1 Efficiency and Distributive Justice in Ordinal Poverty Indices ... 13

1.1 Introduction ... 13

1.2 Theoretical Background ... 15

1.3 The Aggregation Step ... 19

1.3.1 The Fuzzy Set Approach ... 19

1.3.2 The Distance Function Approach ... 20

1.3.3 The Information Theory Approach ... 22

1.3.4 The Axiomatic Approach ... 23

1.4 Correlation-Sensitive Poverty Indices ... 27

1.5 Poverty in India ... 33

1.6 Conclusions ... 38

2 Efficiency and Distributive Justice in Cardinal Poverty Indices ... 40

2.1 Introduction ... 40

2.2 Theoretical Background ... 42

2.3 The Axiomatic Foundation for Cardinal Poverty Measures ... 45

2.4 Inequality-Sensitive Poverty Indices ... 52

2.5 Empirical Application ... 58

2.6 Conclusions ... 61

3 Operationalising the Capability Approach ... 63

3.1 Introduction ... 63

3.2 Theoretical Background ... 66

3.3 The Axiomatic Foundation and Decomposition ... 68

3.4 The German Correlation Sensitive Poverty Index ... 71

3.5 Empirical Application ... 83

3.6 Conclusions ... 95

Bibliography ... 97

Appendix 1 ... 103

Appendix 2 A ... 106

Appendix 2 B ... 110

Appendix 3 A ... 113

Appendix 3 B ... 115

List of Abbreviations

ALEP Auspitz-Lieben-Edgeworth-Pareto

AN Anonymity

BMI Body Mass Index

CSPI Correlation Sensitive Poverty Index CLI Composite Living Index

DIE German Development Institute

DIW German Institute for Economic Research DHS Demographic and Health Surveys

EPC Equality-Promoting Change FD Factor Decomposability FGT Foster-Greer-Thorbecke

GCSPI German Correlation Sensitive Poverty Index GE Generalized Entropy

GSOEP German Socio-Economic Panel IS Inequality Sensitivity

H Headcount

ISPI Inequality Sensitive Poverty Index IT Information Technology

MDG Millennium Development Goals MPI Multidimensional Poverty Index

MN Monotonicity

NDA Nondecreasingness under Association Increasing Switch NIA Nonincreasingness under Association Increasing Switch

NIPA Nonincreasingness under Pareto-efficient Association Increasing Switch

NM Normalization

OPHI Oxford Poverty and Human Development Initiative PP Principle of Population

SCSPI Subjective Correlation Sensitive Poverty Index SD Subgroup Decomposability

SF Strong Focus SI Scale Invariance

SIIS Sensitivity to Inequality Increasing Switch UM Uniform Majorization

UNDP United Nations Development Programme USAID U.S. Agency for International Development WAI Weighted Asset Index

WHO World Health Organization

List of Figures

Figure 0.01 Transforming Economic Resources into Utility ... 4

Figure 0.02 Capabilities and Functionings ... 7

Figure 1.01 Existing Identification Methods ... 18

Figure 1.02 The Correlation Sensitive Identification Method ... 28

Figure 1.03 The Structure of the MPI ... 34

Figure 1.04 Indian Poverty Maps according to MPI and CSPI ... 38

Figure 2.01 The Correlation Sensitive Identification Method ... 44

Figure 2.02 Pareto-Efficiency and Association Increasing Switches ... 49

Figure 2.03 The Structure of the ISPI ... 59

Figure 3.01 The Structure of the GCSPI ... 80

Figure 3.02 Sum of Missing Values 2002-2010 ... 82

Figure 3.07 Headcounts AROPR and GCSPI ... 86

Figure 3.08 Headcounts GCSPI, SCSPI and AROPR Germany 2010 ... 87

Figure 3.09 Development of Economic Figures Germany 2002-2010 ... 88

Figure 3.10 Different Poverty Paths in Germany 2002-2010 ... 90

Figure 3.11 German Poverty Maps AROPR 2002-2010 ... 91

Figure 3.12 German Poverty Maps GCSPI 2002-2010 ... 92

Figure 3.13 German Poverty Maps SCSPI 2002-2010 ... 92

Figure 3.14 Development of Dimensional Decompositions 2002-2010 ... 93

Figure 3.15 Dimensional Decomposition of GCSPI 2010 ... 94

Figure 3.03 Frequency Distribution Satisfaction with Health ... 113

Figure 3.04 Frequency Distribution Satisfaction with Work ... 113

Figure 3.05 Frequency Distribution Satisfaction with Housing ... 114

Figure 3.06 Frequency Distribution Satisfaction with Income... 114

List of Tables

Table 1.01 Axiomatic Foundation of Selected Ordinal Poverty Measures ... 31

Table 1.02 A Comparison of Five Indian Households (DHS 2005) ... 34

Table 1.03 Poverty Rates and Decompositions Selected Indian States ... 35

Table 1.04 The CSPI and Selected Decompositions for India (DHS 2005) ... 36

Table 2.01 Axiomatic Foundation of Selected Cardinal Poverty Measures ... 55

Table 3.01 Spearman Rank Correlation Equal and Prevalence Weights ... 82

Table 3.02 Kendall Tau b Correlation all Dimensions ... 84

Table 2.02 Decomposition FGT ISPI α = 1.5 ... 110

Table 2.03 Decomposition FGT ISPI α = 2 ... 111

Table 3.03 GCSPI Decomposition 2002-2010 ... 115

Table 3.04 AROPR Decomposition 2002-2010 ... 117

Table 3.05 GCSPI Decomposition 2002 (prevalence weights) ... 117

Table 3.06 GCSPI Decomposition 2004 (prevalence weights) ... 118

Table 3.07 GCSPI Decomposition 2006 (prevalence weights) ... 118

Table 3.08 GCSPI Decomposition 2008 (prevalence weights) ... 119

Table 3.09 GCSPI Decomposition 2010 (prevalence weights) ... 119

Table 3.10 GCSPI Decomposition 2002 (equal weights) ... 120

Table 3.11 GCSPI Decomposition 2004 (equal weights) ... 120

Table 3.12 GCSPI Decomposition 2006 (equal weights) ... 121

Table 3.13 GCSPI Decomposition 2008 (equal weights) ... 121

Table 3.14 GCSPI Decomposition 2010 (equal weights) ... 122

Table 3.15 SCSPI Decomposition 2002 ... 122

Table 3.16 SCSPI Decomposition 2004 ... 123

Table 3.17 SCSPI Decomposition 2006 ... 123

Table 3.18 SCSPI Decomposition 2008 ... 124

Table 3.19 SCSPI Decomposition 2010 ... 124

Introduction

‘[W]ealth is evidently not the good we are seeking; for it is merely useful and for the sake of something else’

Aristotle in Nicomachean Ethics (Volume 1, p. 7)

Welfare economics, which according to Amartya Sen ‘is the part of economics that is concerned with the assessment of the goodness of states of affairs and the appraisal of policies’ (Sen, 2009, p. 272), has traditionally equated well-being with happiness, placing the latter at the centre of analysis. The roots of this tradition can be traced back as far as the fourth century BC, to the time of Aristotle. In his two-part ‘philosophy of human affairs’, the Greek philosopher argues that happiness, or Eudaimonia, is the final human good, the one thing every person is striving to achieve (Bartlett and Collins, 2012, p. x). His approach would influence economics for centuries to come, such as the theory of utilitarianism, which typically defines utility as some psychological metric such as happiness or pleasure.

Traditional Welfarism

Utilitarianism, pioneered in 1789 by Jeremy Bentham (Bentham, 2007), continued to provide the basis for welfare economics until well into the nineteen-thirties: traditional welfarism measured the goodness of states of affairs in a society as the sum of individual utilities in that society, thereby building upon the cardinal measurement, comparison and aggregation of individual utilities. It is not hard to see that this is a very ambitious approach, especially considering the fact that utility is a rather fuzzy concept that is already difficult to measure, let alone to compare and aggregate in a fairly reasonable manner.

In fact, it was the assumption of interpersonal comparability of utility that eventually dealt the first major blow to traditional welfare economics in the nineteen-thirties.

Researchers such as the British economist Lionel Robbins argued that interpersonal comparisons of individual (cardinal) utilities cannot possibly be made in any sound scientific sense: ‘I still cannot believe that it is helpful to speak as if interpersonal comparisons of utility

rest upon scientific foundations – that is, upon observation or introspection. I am perhaps more alive than before to the extraordinary difficulties surrounding the whole philosophy of valuation’ (Robbins, 1938, p.640).

At the heart of the problem is the fact that mental conditioning as well as adaptive preferences, whether upward or downward, can have a significant impact on individual utilities (Dworkin, 1981a, pp. 228-240; Sen, 1987, p. 11; Roemer, 1998, pp. 238-239). An example of the former is provided by “expensive tastes”, which refer to the special preferences of an individual who needs more than others in order to reach the same utility level. Assuming equal capacity for satisfaction would disregard this issue – and consequently allocate a larger share of society’s resources to this individual. Another example would be

“offensive tastes”, which denote the special, actually sadistic preferences of an individual who needs to have his or her fellow creatures treated poorly in order to reach the same utility level as others. An example of the latter is what has become known as the “tamed housewife”

scenario, describing a situation in which continuously bad circumstances result in a downward adaptation of preferences, leading to a situation in which individuals need far less than others in order to achieve the same level of utility.

Despite the severe and not easily rejectable criticism, traditional welfarism managed to survive, though in the sharply reduced version of revealed preference welfarism, pioneered by Abram Bergson (1938) and Paul Samuelson (1948). Revealed preference welfarism dissociated itself from any kind of interpersonal (cardinal) utility measurement, comparison and aggregation. Instead, it relied solely on the (ordinal) observable expression of preferences.

However, about ten years later, the slimmed down version of traditional welfarism received a second and this time final blow.

The blow came in the form of what was to become one of the most famous theorems, i.e.

the impossibility theorem of Kenneth Arrow (1950). What Arrow demonstrated is that any policy decision based on revealed preferences with regard to three alternatives or more is unable to satisfy a set of very few reasonable properties. In particular, he introduced the following three axioms: 1. Unrestricted Domain (U), i.e. the domain is defined for the set of all preference orders of the society; 2. Weak Pareto (WP), i.e. whenever all members of a society prefer alternative x to y, then x should be collectively preferred to y as well; 3.

Independence of Irrelevant Alternatives (I), i.e. whenever additional alternatives are offered but do not change any of the individual preference orders, the collective decision should not change either.

Kenneth Arrow’s impossibility theorem demonstrates that in the case of three alternatives or more, any decision rule that satisfies U, WP and I is unable to satisfy another highly desirable property referred to as Non-Dictatorship (ND) which requires that collective decisions are not dictated by the preferences of one individual. This result, astonishing at first glance, is driven by the fact that the restriction on revealed preferences reduces any decision- making process to a voting method of some form or another. However, the exposure of voting methods to a series of consistency problems was recognised almost two hundred years earlier, for instance by the French mathematician and philosopher Marie Jean Antoine Nicolas Caritat, better known as the Marquis de Condorcet. In 1785, he made an observation that was to go down in history as the Condorcet Paradox and that illustrates vividly the consistency problems of voting methods.

Consider, for instance, the following very simple example of the Condorcet Paradox.

Imagine a society with three individuals who have to decide between three different alternatives, i.e. x, y and z. Furthermore, assume that the three individuals have the following preferences over x, y, and z:

2 :

2 :

2 : 3

. 2 . 1 .

x z

z y

y x

y x

z

x z

y

z y

x

Ind Ind

Ind

f f f











Given that the society as a whole prefers x to y (xf y) and y to z (yf z), one would logically expect that x would be preferred to z (xf z), a property that has become known as transitivity. However, in the example above, the society as a whole prefers z to x (zf x) so that any decision based on this society’s voting is inevitably arbitrary and – dictatorial.

Numerous studies worked on rehabilitating revealed preference welfarism, but to no avail. Different versions of the impossibility theorem proved that it applied in one form or another to any social welfare function that was not of the type “cardinally fully comparable”, i.e. the very type whose rejection led to the development of revealed preference welfarism in the first place. This opened the door for alternative approaches.

The Income Approach

Leaving aside those approaches that aimed to replace the whole idea of welfarism, for instance contractarian or libertarian approaches, one concept that is closely related to utilitarian welfare economics seemed to gain broad acceptance was the income approach,

which can be traced back to William Petty (1623-1687), who is acknowledged as the pioneer of national income accounting. It is interesting to note that, as Amartya Sen points out (2009, p. 226), William Petty explicitly mentioned other determinants of individual condition besides income, such as happiness and safety. Likewise, the deliberate restriction that Cecil Pigou imposed when he suggested, as early as 1932, that national income be used to measure ‘that part of social welfare, that can be brought directly or indirectly into relation with the measuring-rod of money’ was largely ignored (Pigou, 2005, p.11).

It seems that after struggling for years with the problem of comparing utility, an easy approach was rather tempting. Concepts such as well-being, poverty, and inequality were almost exclusively measured in monetary terms over the next few decades.

However, the chain from economic resources to utility (whatever the definition²) is anything but straightforward.

Figure 0.01 Transforming Economic Resources into Utility

In response to the theoretical dead-end represented by a concentration on the outcome utility, there has been a shift towards the input economic resources (wealth, income) as the new basis for welfare economics. Aristotle’s statement was rarely contested that economic resources were not an end in themselves but rather means to an end. Specifically, it was assumed that economic resources provided a sufficiently precise proxy for the actual subject matter, i.e. utility. In order for this proposition to hold, two assumptions must be made: that perfect and complete markets exist and that individual conversion factors do not vary, i.e. all

2 In the following, I will define utility as “something that individuals value and have reason to value”, whatever the individual definition of that something may be. Also, I will leave aside the whole question how utility functions might look like as this would go well beyond the scope of this thesis.

Economic Resources

Assumption: equal individual conversion factors

Ignoring (Sen, 2009, p. 255):

- Personal heterogeneities - Variations in physical

environment

- Differences in social climate - Diversity in relational

perspectives

Utility Goods

Assumption: perfect and complete markets Ignoring in particular:

- Role of public goods - Limited access

- Asymmetric information

Choice Conversion

RESPONSE: Primary Goods Index John Rawls (1971) RESPONSE: Insurance MarketRonald Dworkin (1981b)

individuals have the same ability to convert goods into utility. Over the course of time, however, the accuracy of these two assumptions has been increasingly questioned.

With regard to the perfect and complete markets assumption, it was stated that i) especially in developing countries many individuals only have limited access to markets; ii) markets for many of the most basic goods do not exist at all, for instance, public goods such as access to healthcare and education systems; and, finally, iii) due to asymmetric information, prices can neither be considered efficient nor fair. With regard to the assumption of individual conversion factors being equal, Amartya Sen (2009, p. 255) actually provided a whole list of factors influencing the ability of individuals to convert goods into what they have reason to value: i) personal heterogeneities, caused by any kind of handicap or any kind of adversity that individuals might face. A disabled person, for instance, will need more goods and thus more resources than a healthy person in order to live a “normal life”; ii) differences in the physical environment; iii) differences in the social environment; and, finally, iv) diversity in relational perspectives, which refers to a situation in which a person’s absolute standing depends on his or her relative standing compared to other members of society. An example of the latter is provided by Adam Smith: the ability to appear in public without shame, which strongly depends on what Adam Smith calls ‘established rules of decency’

(Smith, 1776, p. 467).

Due to the justified criticism, many researchers have sought time and again to create alternative approaches for a new – and convincing – theory of welfare economics. In an effort to overcome the problems connected with the perfect and complete market assumption, John Rawls introduced in his theory of justice (1971) an index of primary goods which are defined as goods that ‘a rational man wants whatever else he wants’ (Rawls, 1971, p. 79). They are goods that every person needs to have in order to successfully realise his or her individual life plan. The index of primary goods is intended to replace economic resources as the object of analysis in his theory of (social) justice. Whereas Rawls’ index successfully avoids the perfect and complete market assumption, it has some serious weaknesses of its own.

For one thing, it is by no means obvious what these primary goods are that all people want or who should define them. Rawls himself provides five broad categories: ‘rights, liberties, and opportunities, and income and wealth’ (Rawls, 1971, p. 79). It would be difficult to agree on even these broad categories in all cultures, but in order to apply the index in practice, a much more detailed definition would be needed. At the root of the problem is the fact that the removal of the complete and perfect market assumption led to the loss of another aspect, that of individual choice. The objective of the income approach is to ensure that

persons receive a minimum amount of money. However, it is up to them how they actually spend their money. The primary goods approach, on the other hand, leaves no scope for individual choice as it predetermines the goods people ought to have. Even where there is overwhelming consensus on the selection of these primary goods, Rawls’ approach still has a distinct taste of paternalism about it. In addition, it still suffers from the fact that the ability to convert goods into utility can vary greatly from individual to individual. However, any measurement approach that ignores these differences gives a misleading image of individual poverty and consequently leads to distribution policies that are, in fact, unjust (e.g. Sen, 2009, p. 255).

In an effort to overcome the weaknesses of Rawls’ approach, Ronald Dworkin (1981b) developed the idea of a hypothetical insurance market. He draws on John Harsanyi’s concept of ‘choice involving risk’ (1953, p. 435) in which the unborn soul has to choose between different types of income distribution in a society without knowing which social position it will be born into³. Dworkin’s idea is that individuals, behind the veil of ignorance, have the opportunity to buy insurance against any kind of conversion handicap they might experience in their lives. Those who choose to insure themselves will receive compensation for their handicap as determined by the insurance they purchased. With such a hypothetical insurance market in place, so goes the argument of Dworkin, the problem of different conversion factors can be overcome and real equality of resources can be achieved. It should be noted that Ronald Dworkin differentiates between two kinds of inequality. His insurance market provides compensation for inequality that is due to external circumstances, while inequality that is due to individual choices and preferences is not compensated.

One of the main problems of Dworkin’s approach, though, is that while it works rather well in the case of individual handicaps, it is much harder to consider insurance markets for non-personal characteristics (Sen, 2009, p. 266). In addition, his approach also relies on the same perfect and complete market assumption as the income approach.

The Capability Approach

Though both of the aforementioned approaches have become famous theories in social science, neither of them was convincing enough to successfully compete with the highly appreciated simplicity of the income approach. However, another approach has been

3 This concept has become better known in economic literature by the term used by John Rawls in his theory of justice: the ‘veil of ignorance’ (Rawls, 1971, p. 118).

developed that deliberately breaks away from traditional thinking: the capability approach developed by the Indian economist and philosopher Amartya Sen (1979, 1985, 1992, 1999, 2009). Each of the approaches presented so far focuses on the instruments for achieving well- being, a logical consequence following the abandonment of utilitarianism and its failure to make well-being itself the subject of analysis. The novelty of the capability approach is its introduction of so-called functionings and capabilities that are not instruments but constitute elements of well-being (Sen, 1992, p. 39).

Functionings are the “beings” and “doings” individuals are able to be and do (Sen, 1992, p. 39). Functionings are rather different to commodities. They constitute an aspect of living itself whereas commodities are objects a person might use. According to Sen, basic functionings include the ability to be well-nourished, to live a healthy life and to walk about without shame. Whereas a person’s set of functionings represents his or her actual achievements, the set of achievable functioning vectors constitutes that person’s capability set. In other words, a person’s capability set represents his or her freedom to choose between different functioning bundles and thus that person’s opportunities to achieve well-being.

Figure 0.02 Capabilities and Functionings

Through the introduction of capabilities and functionings, the capability approach successfully bypasses the problems associated with the assumptions of perfect and complete markets and of equal individual conversion factors while at the same time introducing two very interesting aspects of individual responsibility and freedom of choice.

The first aspect is introduced by the differentiation between the capability set of possible functioning bundles on one hand and the functioning bundles themselves on the other.

Consider the following example of Amartya Sen (1992, p. 52): Imagine two individuals who are undernourished. One individual is undernourished because he or she is starving, i.e. lacks

Economic Resources

Assumption: equal individual conversion factors

Ignoring (Sen, 2009, p. 255):

- Personal heterogeneities - Variations in physical

environment

- Differences in social climate - Diversity in relational

perspectives

Utility

Assumption: perfect and complete markets Ignoring in particular:

- Role of public goods - Limited access

- Asymmetric information

Choice Conversion Capability Set

Goods Functio-

ning bundle

Choice Choice

the means to satisfy his or her hunger. The other person, however, has enough means to satisfy his or her hunger, but deliberately chooses to fast for religious reasons. Standard theory would treat both individuals the same, however, the capability approach differentiates between the two as they have very different capability sets. While neither may meet a specific minimum calorie intake, the former has no choice but to starve due to a restricted capability set. The latter, on the other hand, has the capability to eat, but out of free choice refuses to do so.

The second aspect is introduced through the fact that though the individually chosen functioning bundles are constitutive elements of utility (or well-being), they can also be utilised to extend the capability set and thus enhance well-being. In other words, a sufficiently large initial capability set enables individuals to pursue well-being, but does not ensure well- being, as the latter is a matter of individual responsibility. It is interesting to note here that when Thomas Jefferson (1743-1826) penned the Declaration of Independence (ratified on the 4^th of July 1776), he seemed to have a similar idea in mind. Up until that point, the prevailing opinion of what rights a government must ensure could be traced back to the British philosopher John Locke (1634-1704), who, in his ‘Second Treatise of Government’ (1690), claimed these rights to be life, liberty and possessions⁴. Thomas Jefferson deliberately replaced the last aspect when he penned: ‘We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.’ It is very interesting that he wrote of the rights to life and liberty, but not the right to happiness. Instead, he called for the right to pursue happiness, acknowledging that happiness itself is something closely bound up with individual responsibility and choice.

Despite the obvious and intriguing advantages of the capability approach, it has not been adopted readily. The reason is that, while undoubtedly intriguing, the theoretical framework of the capability approach is rather difficult to operationalise. For one thing, though the new approach introduces different aspects of choice, it neglects another one, the choice of those

“essential capabilities” that shape the minimum capability set individuals ought to have in order to be able to pursue their goals in life. Sen rightfully claims that this weakness is not as bad as in the case of Rawls’ primary goods approach, as it is much easier to agree on capabilities than on goods (e.g. Sen, 1985, p.6). For instance, it is much easier to agree on the

4 ‘The state of nature has a law of nature to govern it, which obliges every one: and reason, which is that law, teaches all mankind, who will but consult it, that being all equal and independent, no one ought to harm another in his life, health, liberty, or possessions […].’ (Locke, 1690, chapter 2, Sect. 6).

capability to avoid undernourishment than it is to agree on a specific calorie intake. However, he also acknowledges that choosing the essential capabilities is still a difficult and controversial task. Consequently, Sen refused to provide even a list of broad categories that could be used to operationalise his approach. It was the American philosopher Martha Nussbaum who bridged this gap by suggesting ten ‘central human capabilities’ (Nussbaum 2003, pp. 41-42). Though her list is far from uncontested, it is already being widely used to apply the capability approach. The other reason for scepticism towards this approach is the plurality inherent in the nature of capabilities and functionings. Comparing, even aggregating, different functionings or capabilities has been reproached for adding ‘apples and bananas’.

Yet, the capability approach has so many intriguing advantages, especially when it comes to measuring poverty and inequality, that it is beginning to gain traction within the area of welfare economics. This trend is being fuelled further by the empirical applications of the approach, which have provided evidence that it produces rather different results to the traditional income approach (e.g. Klasen, 2000, Alkire and Santos, 2010, Figari, 2012).

Multidimensional Poverty Measurement

As has already been pointed out, what is so fascinating about the capability approach is its approach to freedom of choice and individual responsibility. Poverty, according to Sen, is

‘not a matter of low well-being, but of the inability to pursue well-being’ (Sen, 1992, p. 110).

In order to measure poverty as the inability to pursue well-being, a minimum capability set needs to be determined that comprises those basic or central capabilities that a person needs in order to be able to pursue his or her goals in life, i.e. his or her well-being. The definition acknowledges that the capability or opportunity of the poor to develop their human capital and reach their full potential is limited by external circumstances, such as socio-economic background, race, gender, religion, health, or nutrition.

Likewise, the issue is not inequality of well-being but inequality in the ability to pursue well-being. This definition already indicates Sen’s concern to base considerations of distributive justice, i.e. the ‘deep need for impartiality between individuals’ (Sen 1992, p. 21), on the “right” kind of inequality (Sen, 1997, p. 12). This right kind of inequality is inequality among the poor, or inequality in the opportunity of individuals to pursue whatever they have reason to value. It wastes human capital, not as a result of individual choice, but due to being enforced on people by discrimination of any sort, e.g. by their socio-economic background, race, gender or religion, but also by adversity, such as poor health resulting from sicknesses

or accidents etc. This is the kind of inequality we would want to avoid out of considerations of justice.

The kind of inequality we may not want to avoid is the inequality that results directly from freedom of choice. As an example, consider two individuals with the same capability set, i.e. with the same opportunity to pursue their goals in life. Whereas the first person chooses to enjoy life and work only if unavoidable, the other person makes great efforts to invest in his or her human capital in order to make his or her life count. While it is not in the interest of the capability approach to compare, let alone evaluate, the two different lifestyles, being as they are the result of individual choice, it nevertheless has to ask the question of how to deal with the results of the different choices. It is obvious that the second person will end up with a much larger capability set than the first person, i.e. there will be a high degree of inequality of capabilities.

However, this is a type of inequality that we may not want to fight. The reason is that there exists a tension between the objective of equal capabilities on one hand and the objective of overall expansion of capabilities, which I will refer to as “efficiency”, on the other.⁵ Sen argues, ‘[a]n attempt to achieve equality of capabilities – without taking note of aggregative considerations – can lead to severe curtailment of the capabilities that people can altogether have’ (Sen, 1992, pp. 7-8). Inequality in this case would reward the effort and investments made by the second person that are more than likely to lead to an overall expansion of capabilities from which society as a whole would benefit.

These considerations are strongly corroborated by the results of a recent study by Marrero and Rodriguéz (2010). The authors argue that the reason the relationship between inequality and growth is still controversial in academic literature is that this differentiation between inequality of opportunity and inequality of choice has not been made. Utilising a panel data set for 23 U.S. states, they demonstrate that no significant relationship can be established between overall inequality and growth whereas a robust and significantly positive relationship exists between growth and inequality of choice, and a robust and significantly negative relationship between growth and inequality of opportunity.

5 Please note that there are two ways to apply the concept of efficiency. The first is a dynamic interpretation, i.e.

it refers to the fact that rewarding effort and investments leads to higher growth and thus ‘generally enhancing individual advantages, no matter how distributed’ (Sen, 1992, p. 136). The second one is a static interpretation, i.e. describing a redistribution that improves the advantages of some individuals without worsening the situation of the others. It is the latter interpretation that is utilized in this thesis.

These considerations forcefully demonstrate why inequality among the poor is crucial for any evaluation of poverty and explain Sen’s strong opposition to poverty indices that neglect inequality (Sen, 1992, p. 103):

‘It can now be asked whether the two together would provide an adequate informational base for poverty measurement? The answer, briefly, is: no. H and I [i.e. poverty incidence and intensity] together still cannot be adequate, since neither pays any attention to the distribution of income among the poor. […] Intensification of the more acute deprivation cannot be outweighed by the increase in the income of the person who was less poor even to start with.’

He further argues that by ignoring inequality among the poor, one might very well end up with anti-poverty policies (Sen 1992, p. 105).

But the considerations also explain his claim for a clear distinction between the concepts of distributive justice and efficiency that, though of course closely related, are obviously not the same. Acknowledging the tension between them is crucial. Though efficiency and distributive justice considerations make the same strong case against inequality of opportunity, they might very well differ in their ways of fighting it. In fact, one could easily consider changes in situations that are just, but not efficient and vice versa:

Just, but not efficient: Consider, for instance, a situation with two “comparable”

individuals, i.e. individuals with the same individual characteristics facing the same circumstances. Now assume that one individual has access to seven right shoes and three left shoes, but the other individual has access to three right shoes and seven left shoes. The situation might easily be considered just, as the two otherwise “comparable” individuals have the same capability to wear three pairs of shoes. However, it is also deeply inefficient. By a simple exchange, both individuals could easily expand their capability sets from the opportunity to wear three pairs of shoes to the opportunity to wear five pairs of shoes.

Efficient, but not just: Consider the same initial situation of two “comparable” individuals with seven right and three left shoes and three right and seven left shoes, respectively. Now assume a simple exchange in the course of which individual one hands four of his/her seven shoes over to individual two. Individual one has still the same opportunity to wear three pair of shoes as before, while individual two has now the opportunity to wear seven pairs of shoes.

This exchange is definitely efficient, it is, however, unjust – why should only the second individual gain from the exchange when both individuals could improve their situation?

And yet, current approaches to multidimensional poverty measurement that actually resulted out of Sen’s capability approach do not account properly for his forceful claims.

Well-known and widely-used multidimensional poverty indices either account for distributive justice or for efficiency, treating the two concepts as one and the same and thereby neglecting the tension that exists between them. It is the purpose of this volume to provide ways to overcome this methodological weakness in order to be able to evaluate the changes that a sound operationalisation of the capability approach will induce in poverty measurement.

Efficiency and Distributive Justice in Ordinal Poverty Indices:

The Correlation Sensitive Poverty Index

1 Efficiency and Distributive Justice in Ordinal Poverty Indices

The focus of this chapter is on the two concepts of distributive justice and efficiency within the context of ordinal multidimensional poverty measurement. Though a clear distinction exists between these two concepts they are usually equated. In fact, in the ordinal context inequality between dimensions is usually considered as the spread of simultaneous deprivations across the population. This narrow definition accounts for the concept of distributive justice but not for efficiency. This chapter suggests to define inequality between dimensions as the association-sensitive spread of simultaneous deprivations across the population. This more holistic approach captures both concepts of distributive justice and efficiency and facilitates the introduction of a new axiom as well as a new identification method which in turn provide the basis for a new class of multidimensional poverty indices.

The latter is unique in the sense that it is the first ordinal class of additive poverty indices that is able to take care of considerations of distributive justice and efficiency at the same time. A representative of this class is the Correlation Sensitive Poverty Index (CSPI) that is exemplarily applied to the Indian DHS 2005 data set and illustrates the empirical relevance of the new methodological approach.

1.1 Introduction

The fact that poverty is a multidimensional phenomenon is undisputed, even in the income poverty literature. In fact, income is not supposed to be important per se but rather to serve as an indicator for economic resources that enable individuals to satisfy their multidimensional needs. In order to satisfy that purpose, two main assumptions have to be imposed: i) the existence of complete and perfect markets, and ii) perfect substitutability among all poverty dimensions. The appropriateness of these assumptions, however, has been increasingly

questioned and finally led to a multidimensional measurement approach (e.g. Rawls, 1971;

Sen, 1985; Drèze and Sen, 1989; UNDP, 1995).

Equally undisputed is the fact that inequality is detrimental to poverty reduction and human development in general (e.g. Fields, 1999; Kanbur and Lustig, 1999; Kanbur, 2000;

Ravallion, 2001; White and Anderson, 2001; Bourguignon, 2003; Bourguignon, 2004;

Ravallion, 2007; Grimm et al., 2010). It also nourishes hazardous social tensions and conflicts and even political violence (e.g. Muller and Seligson, 1987; Deininger, 2003). Thus, Sen (1976) requires any reasonable poverty index to be sensitive to inequality. In fact, if poverty is defined as the “lower end” of well-being, then every poverty index is a function of attribute distribution, a fact that shifts inequality into the centre of every poverty analysis.

In a multidimensional framework, poverty attributes are no longer restricted to a perfect substitute relationship. Inequality is no longer confined to the spread of dimension-specific achievements but in addition comprises the joint distribution of attributes across a population.

The former has become known as intra-personal inequality (Kolm, 1977) and has been adequately captured by majorization properties⁶.

This chapter claims that inter-personal inequality (Atkinson and Bourguignon, 1982) – or inequality between dimensions –has not been adequately considered. In fact, in the context of ordinal poverty indices it is commonly equated with the distribution of simultaneous deprivations across the population (Chakravarty and D’Ambrosio 2006, Jayaraj and Subramanian 2010), an equation that fails to consider the relationship that exists between different poverty dimensions. However, the neglect of association-sensitivity leads to a neglect of the concept of efficiency that is not the same as distributive justice – though both concepts are closely related.

In response, this chapter introduces a new property that is based on a broader definition of inter-personal inequality as the association-sensitive spread of simultaneous deprivations across a population, and conditions the extent to which an “inequality increasing switch”

increases poverty on the relationship among attributes. The new property is utilised to derive a new, uniquely characterised class of correlation sensitive poverty indices that is the first ordinal and additive measure able to account for considerations of distributive justice as well as efficiency. In order to demonstrate the empirical implications of the new approach, this chapter closes with a comparison of the poverty rates for 29 Indian states and union territories

6 Majorization properties establish criteria to compare different possibilities to distribute wealth in a society.

Given the two vectors of equal length x=(x₁,...,x_n) and x′=(x₁′,...,x_n′) with

∑

∑

∑

∑

as calculated by of one of the most popular ordinal poverty indices, the Multidimensional Poverty Index (MPI) to those calculated by the new Correlation Sensitive Poverty Index (CSPI).

The chapter proceeds as follows. The second section provides a brief introduction in the theoretical background of the chapter. Section three lays the axiomatic foundation for the derivation and decomposition of the new class of indices that are derived in section four and utilised in the empirical application presented in section five. Section six concludes. Proofs are relegated to the appendix.

1.2 Theoretical Background

Composite poverty indices are derived in two main steps, i.e. the identification step to identify those who are poor, and the aggregation step to aggregate the individual poverty characteristics into the overall poverty index (Sen 1976). This section concentrates on the identification step. In a multidimensional framework, the identification of the poor requires two choices: i) the choice of poverty dimensions, indicators, thresholds and weights in order to identify those who are deprived, and ii) the choice of an appropriate method to identify the poor within the group of the deprived. Though the choices taken in the first step are crucial, they go well beyond the scope of this chapter whose theoretical approach can be applied to whatever poverty dimensions, indicators, weights and thresholds have been chosen in the first step. The following is a summary of the notations and definitions used throughout the chapter.

Let ℝ^k denote the Euclidean k-space, and ℝ^k+ ⊂ℝ^k the non-negative k-space. Further, let ℕ denote the set of positive integers. N={1,...,n}⊂ℕ represents the set of n individuals and

⊂

={2,...,d}

D ℕ the set of d poverty dimensions captured by a set of poverty attributes

⊂

={2,...,k}

K ℕ^{. Let} a∈ℝ^K+ denote the weight vector for the different attributes with a_j >0 for all j=1,...,k and 1.

∑

I refer to the quantity of an attribute with which an individual is endowed as an achievement. The achievement vector of individual i is represented by x_i⋅ =(x_i1,...,x_ik). The achievement matrix of a society with n individuals is represented by X∈ℝ^NK+ where the ijth entry represents the achievement x_ijof individual i in attribute j. Let X_n be the set of possible achievement matrices of population size n and X=U_N⊂_ℕX_n the set of all possible achievement matrices. I further refer to the poverty threshold of attribute j as z_j. Thus, individual i is deprived in attribute j whenever her achievement falls short of the respective threshold, i.e.

whenever x_ij <z_j. z∈ℝ^K++ represents the vector of the chosen poverty thresholds and Z the set of all possible vectors of poverty thresholds.

I define a poverty index as a function P: X _×Z→ℝ. For any poverty threshold vector Z

z∈ , society A has a higher poverty level than society B if and only if ^P

(

)

(

)

for any X^A,X^B∈X_.

The main methods for the identification of the poor are the aggregate poverty line approach and the component poverty approach. Under the aggregate poverty line approach, the identification of the poor is based upon a function ϕ:ℝ^{k ×}ℝ^k →ℝ that aggregates individual achievements in all poverty dimensions. A person is poor if and only if his/her aggregation function is negative, i.e. ϕ

(

)

This limits the application of this approach to a cardinal context and does therefore not allow an ordinal-cardinal comparison as aspired in this volume.

Therefore, the following analysis is based upon the second method, the component poverty approach that builds upon an attribute-wise evaluation of poverty. All attributes are considered to be essential in the sense that a failure to achieve the threshold level automatically implies deprivation no matter what the achievements are in other dimensions, i.e. compensation is restricted to attributes below threshold levels (Strong Focus Axiom). In order to describe the component poverty approach, let c_i⋅=(c_i1,...,c_ik) represent the deprivation vector of individual i such that c_ij =1 if x_ij < z_j and c_ij =0 if x_ij ≥z_j. Further, let

{

∑

=

∈

=

1 : ,..., 1 k c_ij j

j

i a

δ denote the sum of weighted deprivations suffered by individual i and let

( )

Sj – or simply S_j– denote the set of individuals who are deprived with respect to attribute j. The identification of the poor is based on a function ρ: ℝ^K+ ×ℝ^K++ →{0,1}, i.e. an identification function such that individual i is poor if ρ(c_i⋅;z)=1 and not poor if

0 )

; (c_i⋅ z =

ρ .

Three specifications of the identification function have been suggested so far. The union method is based on the (rather strong) assumption that all attributes are perfect complements⁷.

7 I follow the Auspitz-Lieben-Edgeworth-Pareto (ALEP) definition of substitutability and complementarity. The ALEP definition considers two attributes to be substitutes if their second cross partial derivatives are positive.

Intuitively, an increase in one attribute decreases poverty the less the higher the achievements in the second attribute. In the same way, attributes are considered to be complements, when the respective cross partial derivatives are negative and independent in case they are zero.